1. Field of the Invention
The present invention relates to the field of oil exploration, and more particularly to the study of the geological history of oil systems, within a sedimentary basin.
2. Description of the Prior Art
Basin modeling attempts to reconstruct the geological history of a sedimentary basin and of its oil systems so as to help to locate hydrocarbon traps, that is reservoirs, to estimate their quantity and quality, and finally, to evaluate the risks of encountering excess pressures during drilling operations. These objectives are achieved by studying the burial history of sediments, their thermal history, the kinetics of the formation of the hydrocarbons, and the migration (flow) of the hydrocarbons.
Such a study is carried out by means of two types of tools: on the one hand software, called a basin simulator, makes it possible to solve systems of ordinary or partial differential equations solved by various numerical schemes; and on the other hand a dynamic mesh describing the geometrical evolution of the basin concerned, and on which the systems of equations are solved.
Today, exploration is involved with zones of complex geometry where the faults are numerous and their location random. The automatic construction of a 3D mesh capable of representing this geometrical complexity is the first indispensable step in the formulation of a representation of such a medium, on the basis of horizons which delimit the various geological layers and faults which cut the horizons. The horizons and the faults are provided as surfaces, triangulated on the basis of a scattering of points resulting from seismic surveys.
In the world of oil exploration, most basin simulators operate on regular or “Scottish Cartesian” meshes. To attempt to adapt the meshes to the faults and to all forms of heterogeneities, as a support for the calculation of the simulation, the technique of local grid refinement is known, the technique of CPG grids (described in document FR 2 747 490 for example), or else the technique of grids with vertically split nodes is used.
The meshes described above are based on grids. They are nearly structured. That is to say their inter-vertex relation is fixed. Each internal vertex is incident at a fixed number of mesh cells and each mesh cell is delimited by a fixed number of faces and edges. They are thus suitable only for a relatively simple geometry. For a basin simulator, such as the TemisFlow® software (IFP, France), for each given age, a mesh is constructed by stacking layers, represented on one and the same 2D grid (map), which are joined by verticals. The construction of the mesh is very simple but however, it is impossible to represent faults which are often oblique.
To be able to handle faults, there are methods which first perform a manual blockwise decomposition following faults, and then generate a simple mesh for each block. Such is the case for the RML® software (IFP, France). This approach is, however, not completely suitable for the simulation of flow in a medium with complex geometry for two reasons: First, the quality of elements is not satisfactory for irregular geometries; and second, with the numerous and random presence of faults, it is almost impossible to perform the manual decomposition of the involved medium.
To properly reproduce all the complexity of the geometry of the medium, it is also possible to construct an entirely unstructured mesh, with a completely arbitrary inter-vertex relation. A vertex of the mesh can belong to any number of mesh cells and each mesh cell can possess any number of edges or faces. References may be made for example to the meshes of the PErpendicular Bisector (PEBI) or Voronï type, proposed in:
Z. E. Heinemann, G. F. Heinemann and B. M. Tranta, “Modelling Heavily Faulted Reservoirs”, Proceedings of SPE Annual Technical Conferences, pages 9-19, New Orleans, La., September 1998, SPE.
Although they describe complex geometries well, unstructured meshes are very unwieldy to construct, to manipulate and to store, in contradistinction to structured meshes. To reconcile between the advantages and drawbacks, so-called “hybrid” approaches have been proposed which use unstructured meshes only in zones of complex geometry. Nevertheless, placing unstructured meshes together with structured meshes remains a difficult task.
In the general literature, four major categories of method exist for automatically generating hex-dominant meshes. They are:                the octree/grid methods,        the plastering methods,        the blockwise methods,        the sweep-based methods.        
The principle of octree/grid methods wraps the domain to be meshed in a grid, and subdivides this cube recursively until the geometry of the domain is well captured. That is to say, until the criterion of the size of the mesh cells, which depends essentially on the minimum distance of the points of the contour and resources available, are fulfilled. Tetrahedral or hexahedral elements are then created at the intersection of the surfaces of the domain by following certain intersection patterns.
The octree/grid methods are advantageously automated and applicable regardless of the geometry. However, the generated mesh does not conform to the shape of the domain. Moreover, when the contour is irregular, an intense calculation of intersections is inevitable and an explosion in the number of mesh cells could occur in order to attain a good accuracy of approximation of the boundaries.
The methods of plastering type fill the volume of the domain with 3D elements starting from the initial surface front of the model and advancing towards the center while starting again from the new front which has just been constructed. The procedure terminates once the front becomes empty.
In plastering algorithms, it is difficult to determine the orders of advance of the front and to detect and process the collision and divergence zones. These methods are thus considered to be non-robust. Especially when complex geometries are concerned, the obtaining of a mesh of good quality is not guaranteed.
The blockwise approaches decompose the domain into coarse blocks having an elementary inter-vertex relation (triangle, quadrangle, tetrahedron, pentahedron, and hexahedron), and then in meshing each block independently of one another by algebraic methods or by solving PDEs and in connecting the blocks back together at the end in order to form the global mesh of the entire domain.
The major advantage of block methods is that it is trivial to mesh once the partition is completed. Moreover, it is possible to solve the problem in parallel on each block. However, the partition itself remains very unwieldy and difficult to automate, and the inter-block interfacing must be carefully handled to ensure the conformity of the final sticking together.
Sometimes considered as 2.5D meshing, the sweep-based methods “sweep” a quadrilateral mesh by following a curve. Regular layers of hexahedra are formed at a specified interval using the same inter-vertex relation as the quadrilateral mesh. This technique can be generalized to mesh volumes of certain classes by definition of the source and target surfaces.
The meshes generated by the sweep methods are automatically aligned with the interfaces which is obviously a major advantage. However, these methods are not well suited in the context of simulating a porous medium, where a change of inter-vertex relation may occur from one horizon surface to another on account of the occurrence of faults.